U.S. patent application number 15/447934 was filed with the patent office on 2017-09-21 for designs and manufacturing methods for lightweight hyperdamping materials providing large attenuation of broadband-frequency structure-borne sound.
The applicant listed for this patent is Ohio State Innovation Foundation. Invention is credited to Ryan L. Harne.
Application Number | 20170268591 15/447934 |
Document ID | / |
Family ID | 59855688 |
Filed Date | 2017-09-21 |
United States Patent
Application |
20170268591 |
Kind Code |
A1 |
Harne; Ryan L. |
September 21, 2017 |
DESIGNS AND MANUFACTURING METHODS FOR LIGHTWEIGHT HYPERDAMPING
MATERIALS PROVIDING LARGE ATTENUATION OF BROADBAND-FREQUENCY
STRUCTURE-BORNE SOUND
Abstract
A hyperdamping inclusion under constraint with large, broadband
frequency damping properties is disclosed. The inclusion includes
materials under near-buckling constraint such that fundamental
eigenfrequency vanishes at near-buckling.
Inventors: |
Harne; Ryan L.; (Columbus,
OH) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Ohio State Innovation Foundation |
Columbus |
OH |
US |
|
|
Family ID: |
59855688 |
Appl. No.: |
15/447934 |
Filed: |
March 2, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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62302405 |
Mar 2, 2016 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
F16F 1/3605 20130101;
F16F 7/108 20130101 |
International
Class: |
F16F 7/108 20060101
F16F007/108 |
Claims
1. A wave attenuation device, comprising: an elastic metamaterial;
at least two voids in the elastic metamaterial; the elastic
metamaterial under a stress constraint such that the elastic
material is near a buckling condition.
2. The wave attenuation device according to claim 1, further
comprising an external shell around a portion of the elastic
metamaterial, wherein the external shell provides the stress
constraint.
3. The wave attenuation device according to claim 1, wherein the
elastic metamaterial comprises an elastomer.
4. The wave attenuation device according to claim 3, wherein the
elastomer comprises at least one of natural rubber, synthetic
rubber, butyl rubber, silicone rubber, butadiene rubber, neoprene,
fluoroelastomer, thermoplastics, elastin, resilin, polysulfide,
thermoset, and polyurethane.
5. The wave attenuation device according to claim 1, further
comprising an internal mass having a greater density than the
elastic material.
6. The wave attenuation device according to claim 1, further
comprising poroelastic foam surrounding the elastic metamaterial
under stress constraint.
7. A wave-attenuated structure, comprising: at least one
load-imparting boundary; a wave attenuation device, comprising an
elastic metamaterial having at least two voids in the elastic
metamaterial, the elastic metamaterial under a stress constraint
such that the elastic material is near a buckling condition;
wherein the stress constraint is provided by the at least one
load-imparting boundary.
8. The wave-attenuated structure according to claim 7, wherein the
elastic metamaterial comprises an elastomer.
9. The wave-attenuated structure according to claim 8, wherein the
elastomer comprises at least one of natural rubber, synthetic
rubber, butyl rubber, silicone rubber, butadiene rubber, neoprene,
fluoroelastomer, thermoplastics, elastin, resilin, polysulfide,
thermoset, and polyurethane.
10. The wave-attenuated structure according to claim 7, further
comprising an internal mass having a greater density than the
elastic material.
11. The wave-attenuated structure according to claim 7, further
comprising poroelastic foam surrounding the elastic metamaterial
under geometric constraint.
12. A wave attenuation device, comprising: a hollow metal shell
having a cross-sectional shape having a first dimension; and
elastomeric material within the metal shell and having a
cross-sectional shape mimicking the first cross-sectional shape,
the elastomeric material having a second dimension, the second
dimension greater than the first dimension in a fully expanded
state and a third dimension less than the first dimension in a
compressed state within the metal shell.
13. The wave attenuation device according to claim 12, wherein the
cross-sectional shape is a circle such that the hollow metal shell
is a cylinder and the elastomeric material has a cylindrical
profile.
14. The wave attenuation device according to claim 13, wherein the
elastomeric material comprises a plurality radially-arrayed
beams.
15. The wave attenuation device according to claim 13, wherein the
elastomeric material comprises an inner core, radially-arrayed
beams and an outer cylinder such that a plurality of hollows are
formed between the core, the radially-arrayed beams and the outer
cylinder.
16. The wave attenuation device according to claim 12, further
comprising cutouts in the elastomeric material such that a metal
shell with the elastomeric material with cutouts has a mass less
than 50% of the mass of the metal shell with a solid cylinder of
elastomer therein.
17. The wave attenuation device according to claim 12, further
comprising cutouts in the elastomeric material such that a metal
shell with the elastomeric material with cutouts has a mass about
48% of the mass of the metal shell with a solid cylinder of
elastomer therein.
18. The wave attenuation device according to claim 12, further
comprising a metal mass in the elastomeric material.
19. An acoustic and/or elastic wave attenuation structure,
comprising: poroelastic foam: at least one damping inclusion
comprising: a hollow metal shell having a cross-sectional shape
having a first dimension; and elastomeric material within the metal
shell and having a cross-sectional shape mimicking the first
cross-sectional shape, the elastomeric material having a second
dimension, the second dimension greater than the first dimension in
a fully expanded state and a third dimension less than the first
dimension in a compressed state within the metal shell.
20. The wave attenuation device according to claim 19, wherein the
cross-sectional shape is a circle such that the hollow metal shell
is a cylinder and the elastomeric material has a cylindrical
profile.
21. The wave attenuation device according to claim 20, wherein the
elastomeric material comprises a plurality radially-arrayed
beams.
22. The wave attenuation device according to claim 20, wherein the
elastomeric material comprises an inner core, radially-arrayed
beams and an outer cylinder such that a plurality of hollows are
formed between the core, the radially-arrayed beams and the outer
cylinder.
23. The wave attenuation device according to claim 19, further
comprising cutouts in the elastomeric material such that a metal
shell with the elastomeric material with cutouts has a mass less
than 50% of the mass of the metal shell with a solid cylinder of
elastomer therein.
24. The wave attenuation device according to claim 19, further
comprising cutouts in the elastomeric material such that a metal
shell with the elastomeric material with cutouts has a mass about
48% of the mass of the metal shell with a solid cylinder of
elastomer therein.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to U.S. Provisional Patent
Application No. 62/302,405, filed Mar. 3, 2016, which is hereby
incorporated by reference in its entirety for all purposes as if
fully set forth herein.
BACKGROUND OF THE INVENTION
[0002] Field of the Invention
[0003] Embodiments of the present invention relate to damping
materials having reduced weight than alternative material
selections, and more specifically hyperdamping materials and
inclusions for application in a variety of structures.
[0004] Background
[0005] The absorption or attenuation of spectrally broadband
vibration and wave energy are goals that have called upon the
efforts of researchers spanning diverse engineering and scientific
disciplines over the years. While resonant phenomena can facilitate
striking vibroacoustic energy trapping, many scenarios involve
wide-band or stochastic energy sources for which broadband energy
capture is necessary. Typically, the only assured solution for
broadband energy attenuation is to introduce excessive mass between
the dynamic energy source and the region/receiver of interest,
which conflicts with requirements for many applications, such as
vehicular systems, where added mass is detrimental to performance
and effectiveness. In addition, while input energies may cause
vibrations at low frequencies associated with modal oscillations,
practical structures transfer the energy to higher frequencies due
to joints, friction, and complex geometries, thus creating a `noise
problem` in a bandwidth most sensitive to humans through inevitable
structure-fluid interaction. Although conventional noise control
treatments such as lightweight, poroelastic media are well-suited
to dampen waves in this mid-to-high frequency range, they are
ill-suited to attenuate low frequency vibrations and sound within
typical size constraints. As a result, there is a need for
lightweight materials to dampen spectrally broadband vibroacoustic
energies.
[0006] To address the challenges, strategically architected
material systems have been explored that provide elastic and
acoustic wave attenuation capabilities not otherwise found in bulk
structural materials. Among them, resonant metamaterials and
phononic crystals exhibit opportunities to suppress vibration and
wave energies due to tuned-mass-damper or bandgap effects. However,
despite the advancements, the energy attenuation properties are
reliant upon resonance- or bandgap-related phenomena that are often
parameter sensitive and narrowband. In addition, many experimental
realizations have been proposed using heavy materials including
metals and dense rubbers, which are inadequate solutions in the
numerous practical applications where treatment weight is a great
penalty.
[0007] Building upon these ideas, periodic, elastic metamaterials
leveraging instability mechanisms are shown to yield remarkable
wave propagation control and energy absorption capabilities due to
energy changes associated with transitions among internal
topologies. On the other hand, these elastic systems are likewise
realized by dense materials such as silicones or 3D-printed
polymers that are ill-suited for applications where increased
treatment density comes at a high cost due to the weight they add
to finished products. Static stresses or exterior displacement
constraints may also be needed to achieve the wave tailoring
properties through the buckling instability, which prevents
implementing such metamaterials as absorbers of free field acoustic
energy, in the operational mode similar to conventional poroelastic
foams. In fact, it is well-known that buckling instability-based
phenomena can enhance energy dissipation properties. Such anomalous
damping is due to a cancellation of the positive and negative
stiffnesses, a design condition termed the elastic stability limit,
which eliminates the fundamental natural frequency
.omega..sub.n.fwdarw.0.
[0008] Yet, despite the recent advancements the reliance upon
parameter-sensitive resonance-related phenomena, the use of dense
materials, and possible need for exterior material constraints,
make these concepts insufficient solutions for applications
demanding lightweight materials for broadband vibration and
acoustic energy capture.
[0009] With a different material design perspective in mind, other
recent studies show that heterogeneous, poroelastic metamaterials
can achieve considerable wave and/or vibration energy absorption.
For instance, randomly embedding solid, metal inclusions into
poroelastic foams improves the low frequency attenuation of the
host media. Periodically distributing such inclusions also spawns
bandgap phenomena to substantially increase low frequency
vibroacoustic energy absorption via "trapped" mode effects. On the
other hand, such advancements lack broadband vibroacoustic energy
dissipation in a lightweight system design; instead, these
poroelastic metamaterials excel at one or another of the individual
performance measures.
BRIEF SUMMARY OF THE INVENTION
[0010] Accordingly, the present invention is directed to designs
and manufacturing methods for lightweight hyperdamping materials
providing large attenuation of broadband-frequency structure-borne
sound that obviates one or more of the problems due to limitations
and disadvantages of the related art.
[0011] An advantage of the present invention is to provide a wave
attenuation device, comprising an elastic metamaterial with at
least two voids in the elastic metamaterial where the elastic
metamaterial under a geometric or stress constraint such that the
elastic material is near a buckling condition
[0012] In another aspect of the present invention andfurther
embodiment of the hyperdamping materials, a wave-attenuated
structure, includes at least one load-imparting wall; a wave
attenuation device, comprising an elastic metamaterial having at
least two voids in the elastic metamaterial, the elastic
metamaterial under a geometric or stress constraint such that the
elastic material is near a buckling condition; wherein the
constraint is provided by the at least one load-imparting wall.
[0013] In another aspect of the present invention and further
embodiment of the hyperdamping materials, a wave attenuation device
includes a hollow metal shell having a cross-sectional shape having
a first dimension; and elastomeric material within the metal shell
and having a cross-sectional shape mimicking the first
cross-sectional shape, the elastomeric material having a second
dimension, the second dimension greater than the first dimension in
a fully expanded state and a third dimension less than the first
dimension in a compressed state within the metal shell.
[0014] Further embodiments, features, and advantages of the
hyperdamping materials, as well as the structure and operation of
the various embodiments of the hyperdamping materials and devices,
are described in detail below with reference to the accompanying
drawings.
[0015] It is to be understood that both the foregoing general
description and the following detailed description are exemplary
and explanatory only, and are not restrictive of the invention as
claimed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] The accompanying figures, which are incorporated herein and
form part of the specification, illustrate lightweight hyperdamping
materials according to principles of the present invention.
Together with the description, the figures further serve to explain
the principles of the lightweight hyperdamping materials described
herein and thereby enable a person skilled in the pertinent art to
make and use the hyperdamping materials.
[0017] FIG. 1a illustrates a side view of a hyperdamping inclusion
according to principles of the present invention in disassembled
form.
[0018] FIG. 1b shows finite element model results that predict
rotational motions for pre- and post-buckled designs.
[0019] FIG. 2A illustrates a side view of a hyperdamping inclusion
according to principles of the present invention.
[0020] FIG. 2B illustrates spring forces associated with the
illustrated hyperdamping inclusion.
[0021] FIG. 3 illustrates hyperdamping inclusions according to
principles of the present invention embedded in a poroelastic
material.
[0022] FIG. 4 is a finite element analysis plot for a hyperdamping
inclusion according to principles of the present invention.
[0023] FIGS. 5A and 5B show a hyperdamping metamaterial specimen
according to principles of the present invention prior to
assembly.
[0024] FIG. 6 shows force transmissibility and absorption
coefficient experiment schematics.
[0025] FIG. 7 presents the results of force transmissibility
amplitude and acoustic absorption coefficient
[0026] FIG. 8 shows that the broadband energy absorption and
attenuation is prominent across the range of about 175-225 Hz.
[0027] FIG. 9 shows measurements of absorption coefficient.
[0028] FIG. 10 shows a comparison of eigenfrequency variation among
the four lowest eigenfrequencies and the corresponding mode
shapes.
[0029] FIG. 11 illustrates eigenfrequency distribution and
corresponding kinetic energy density of finite element analyses of
materials according to principles of the present invention.
[0030] FIG. 12 shows force transducers used in experimental testing
of materials according to principles of the present invention.
[0031] FIG. 13 shows an impedance tube setup used in experimental
testing of materials according to principles of the present
invention.
[0032] FIG. 14 is a graph illustrating absorption coefficient
performance of an exemplary hyperdamping inclusion according to
principles of the present invention versus a control inclusion and
poroelastic foam alone.
[0033] FIG. 15 is a graph illustrating force transmissibility
performance of an exemplary hyperdamping inclusion according to
principles of the present invention versus a control inclusion and
poroelastic foam alone.
[0034] FIG. 16 is a graph illustrating one-third octave ban
measurements of force transmissibility of an exemplary hyperdamping
inclusion according to principles of the present invention versus
poroelastic foam alone.
[0035] FIG. 17 illustrates an exemplary use for inclusions
according to principles of the present invention.
[0036] FIG. 18 illustrates an exemplary use for inclusions
according to principles of the present invention.
[0037] FIG. 19 illustrates an exemplary use for inclusions
according to principles of the present invention
DETAILED DESCRIPTION OF THE INVENTION
[0038] Reference will now be made in detail to embodiments of the
hyperdamping materials with reference to the accompanying figures,
in which like reference numerals indicate like elements.
[0039] It will be apparent to those skilled in the art that various
modifications and variations can be made in the present invention
without departing from the spirit or scope of the invention. Thus,
it is intended that the present invention cover the modifications
and variations of this invention provided they come within the
scope of the appended claims and their equivalents.
[0040] According to principles of the present invention, a new
class of engineered material system provides large,
broadband-frequency energy damping properties --hyperdamping.
Furthermore, the "engineering" of the material system according to
principles of the present invention removes mass from the baseline,
non-engineered material, such that these new hyperdamping materials
are also lighter in weight than conventional materials. These
advantages--lightweight, and high damping across broad frequency
bandwidth--are desirable in numerous applications, including
vehicular, architectural, and infrastructural applications where
such performance measures are typically at-odds. The important
consequence of the elastic stability limit for hyperdamping systems
according to principles of the present invention is that the
damping ratio grows without bound according to the classic relation
for the fundamental modal damping ratio .zeta.=c/2m.THETA..sub.n
where c and m are the modal damping constant and mass,
respectively. Exemplary embodiments of design and fabrication
procedures of hyperdamping materials according to principles of the
present invention are provided herein. In addition, experimental
measurements to demonstrate the performance of the various
embodiments are provided, although are not meant to be limited to
the scope of the invention.
[0041] An exemplary embodiment of "hyperdamping inclusion" 10 is
illustrated in FIG. 1. FIG. 1(a) shows a hyperdamping inclusion 10
design according to principles of the present invention such that
the elastomer element 12 outer diameter D.sub.o is greater than the
inner diameter D.sub.i of the rigid, metal shell 11. FIG. 1(b)
shows finite element model results that predict rotational motions
for pre- and post-buckled designs. FIG. 2 illustrates that a whole
inclusion rotation is exhibited for increasing degree of
pre-compression upon inserting the elastomer/mass 12 into the metal
shell 11, such that the inner elastic 14 or metallic center masses
16 rotate. FIG. 3 illustrates a hyperdamping metamaterial 24 with
embedded inclusions 20 in poroelastic media 24 to attenuate and
absorb incident acoustic waves 26 and structural vibrations 28.
[0042] According to principles of the present invention, beam-like
sub-components 18 are constrained in a way that causes them to
nearly buckle. For example, the elastomer inclusions 10 illustrated
in FIGS. 1, 2A and 2B include the radially arrayed beams 18 that
are constrained geometrically by virtue of the outer shell 11 and
inner lumped mass 14. For instance, the lumped mass 14 in FIG. 1(a)
is the central cylinder of elastomer out of which the
radially-arrayed beams 18 extend. Such near-buckling can be
realized in any material system that can be "architected" with
beam-like internal geometries. This includes laser cutting into
metal, wood, and so on such geometric features and have those
material components serve under constraint or static pre-load (that
gives similar effect as constraint).
[0043] As illustrated, the exemplary device includes an elastomer
inclusion. The elastomer inclusions are in a pattern with
radially-arrayed beams extending from a central, lumped elastomer
mass. Namely, a soft, cylindrical and sculpted elastomer element is
inserted into a metal shell 11 that has an inner diameter D.sub.i
smaller than the element's outer diameter D.sub.o, as illustrated
in FIG. 1a. This configuration is intended to load the elastomer
topology at the elastic stability limit. FIG. 1b shows finite
element modeling results to illustrate stable, post-buckled
topologies of the elastomer element if the constraint induces a
stress beyond criticality.
[0044] The elastomer/mass may be inserted into a shell that extends
the same length of the elastomer inclusion. This shell
geometrically constrains the elastomer structure. For example, the
outer elastomer diameter is greater than the inner diameter of the
shell. D.sub.o/D.sub.i>1. This chosen diameter ratio results in
the radially-arrayed beams 18 of the inclusion 10 nearly buckling
under the geometric constraint. This strategic constraint underlies
the high damping, because beams 18 compressed at this so-called
"elastic stability limit" possess an infinitely large damping ratio
due to the elimination of the fundamental elastic stiffnesses. The
uses of hyperdamping inclusions 10 according to principles of the
present invention are many-fold. For example, as illustrated in
FIG. 3, the inclusions 20 may be embedded into a soft, poroelastic
foam 24 where they attenuate structure-borne sound by the local,
yet unusually greatly damped, resonances they undergo in
consequence to the effective stiffness and damping of the host foam
material. Such applications would include acoustic barriers or
panels in residential or vehicular applications. According to
principles of the present invention, it is also possible that the
constraint condition is imposed by surrounding structure in lieu of
the disclosed metal shell. That is, external stress can provide the
near-buckling condition that underlies the damping properties of
the beam-like structure of the elastomer element structure.
[0045] Depending on the design of internal elastomer elements, such
as with or without a solid metal cylinder 16, buckling may or may
not occur for given sizes of the metal shell 11, such as those
illustrated in FIG. 2. Such factors establish a versatile means for
hyperdamping inclusion 10 design and tuning.
[0046] Developed in this way and considering the shell 11 to be
fixed, the hyperdamping inclusion is an extremely damped
spring-mass, as illustrated schematically by FIG. 2B, having a
vanishingly small natural frequency, where mass contributions are
from the internal elastomer 14 and other internal constituents,
such as the metal cylinder shown in FIGS. 2A and 3, in which the
illustrated "springs" refer to the critically-loaded,
radially-arrayed beams 18 of the inclusion 10/20. The inherent
damping constant of this equivalent oscillator is that associated
with the elastomer, and the relative impact of the finite damping
grows upon loading the inclusion at the elastic stability limit. To
leverage the inclusion for wave energy capture, a hyperdamping
inclusion 20 according to principles of the present invention may
be embedded into poroelastic foam 24 where the total inclusion mass
(i.e. the shell 11 and what is within) generates an additional
mass-spring-damper degree-of-freedom (DOF) due to the host media
24, as illustrated in FIG. 3. Two resulting natural frequencies of
this equivalent two DOF system occur at a vanishingly-small value
due to the critically buckled constituent and at a (typically low)
frequency associated with the total inclusion mass and host media
properties. Thus, from an observer's perspective, the lightweight
inclusion according to principles of the present invention responds
dynamically like an extremely damped single DOF that yields massive
vibroacoustic energy damping in a broad frequency bandwidth around
and above the low natural frequency associated with the total
inclusion resonance. Thus, by leveraging a critically-loaded
"hidden" DOF, the hyperdamping metamaterial exhibits beneficial
levels of vibration and wave energy attenuation and absorption
using a lightweight design that interfaces with the acoustic free
field and does not rely on purely resonant phenomena to provide its
effects. Here, the term "metamaterial" refers to an engineered
material system that exhibits non-natural properties by virtue of
"hidden" internal constituents.
[0047] There is no limitation on the use of this concept with
elastomeric materials. The inclusions may be formed of any suitable
elastomer, including, but not limited to, natural rubber, synthetic
rubber, butyl rubber, silicone rubber, butadiene rubber, neoprene,
fluoroelastomer, thermoplastics, elastin, resilin, polysulfide,
thermoset, polyurethane, or the like. The elastomeric material
making up the inclusion according to principles of the present
invention are not limited to this list. The pattern may be formed
by sculpting, injection molding, extrusion, 3-D printing, or the
like. For example, the elastomer inclusion may be made by providing
the elastomer in a mold that is created in the negative of the
desired inclusion shape. Thus, once the elastomer cures in the
mold, the removed component possesses the design features of
interest. A, central mass 14 or 16 may also be provided in the
elastomer inclusion 10, as shown in FIG. 2. The central mass may
include metal, ceramic, plastic, or other material providing
suitable mass in the inclusion.
[0048] An exemplary process for fabricating hyperdamping materials
according to principles of the present invention is described
herein. The fabrication of the hyperdamping metamaterials is
undertaken in several steps. For example, a 3D printer (such as,
but not limited to, FlashForge Creator Pro) generates acrylonitrile
butadiene styrene (ABS) molds that are the negative of the desired
elastomer elements. Silicone (such as, but not limited to,
Smooth-On, Inc., Mold Star 15S) is poured into the molds that may
be previously sprayed with a release agent (such as, but not
limited to, Smooth-On, Inc., Ease Release 200). The samples are
removed after the recommended curing time for the material used has
elapsed. In the exemplary embodiment, elastomer samples are cut to
19 mm length and allowed to set at room temperature for a
sufficient time prior to further use. If the elastomer samples
include interior metal cylinders (e.g., 6.35 mm outer diameter and
19 mm length) such as the samples shown at right in FIG. 2, the
cylinders are held in place in the mold so that the silicone cures
around the cylinder.
[0049] In prepared samples according to principles of the present
invention, several samples of a given outer elastomer diameter
D.sub.o were produced (ranging from D.sub.o.di-elect
cons.[16.38,18.16]mm), whether with solid elastic interior masses
or with interior metal cylinders. The elastomer elements produced
by this method exhibited a mean standard deviation of outer
diameter of 69 .mu.m, which is on the order of the reported
resolution of the 3D printer. The mean mass of the inclusions with
elastomer and metallic internal masses are 3.42 g and 8.04 g,
respectively. Aluminum shells of inner diameter D.sub.i=16.56 mm
and thickness 1.25 mm are cut to 19 mm lengths and the elastomer
elements are carefully inserted into the shells. Sample inclusions
10 made according to this exemplary process include seven
rotationally-symmetric voids 17, as shown in FIG. 1. Inclusions
made according to principles of the present invention can include
any number of voids 17. Performance of inclusions with at least two
voids to realize an annular region around the interior mass such
that the mass is capable of buckling under the displacement
constraint imposed by the metal shell or other structure, are
described herein.
[0050] A finite element (FE) model is useful to develop insight on
inclusion topological designs that maximize the effective damping
properties of the components once embedded into the poroelastic
media. An exemplary a finite element model may be composed using
the commercial software package, such as COMSOL Multiphysics. The
elastomer element designs of interest are those that are loaded
around at the elastic stability limit once constrained within the
metal shells, such that the softening influences are most
prominent. In other words, the elastomer elements are intended to
be extremely close to the point of buckling to maximize the
effective damping properties when the inclusion (shell and
elastomer element) is embedded into the poroelastic foam. As
previously shown, the resonance of the embedded inclusion in the
foam is influenced by factors that consider such inclusions as
equivalent lumped masses within a distributed elastic media. The
rotational symmetry of the molded elastomer designs considered here
is based on the finding that applied stress on an
instability-driven periodic metamaterial induces a symmetry
breaking at the critical buckling stress, as illustrated by FIG.
1b. Although several design parameters may be tailored to sculpt
the topology in ways that provide means to critically stress the
elastomer elements, the focus in this example is on changing the
diametric ratio D.sub.o/D.sub.i and the ratio of rotation angles
.alpha./.beta. in an elastomer element having seven voids, top of
FIG. 4. The rotational angle ratios .alpha./.beta. considered are
set by the limits of fabrication using the current or available
practice, while the diametric ratios D.sub.o/D.sub.i must be >1
to induce buckling.
[0051] Referring to FIG. 4, an illustration at the top right shows
the design parameters of the diametric ratio D.sub.o/D.sub.i and
the rotational angle ratio .alpha./.beta.. The surfaces show the
influence on the fundamental eigenfrequency of the elastomer
element by tailoring these parameters. The upper surface considers
the elastomer element with the same internal elastomer mass, while
the lower surface considers the metallic mass in the elastomer
element.
[0052] As observed in the finite element model results in FIG. 4,
the decrease of the absolute value of the lowest eigenfrequency,
which vanishes at the buckling point, may span orders of magnitude
via tailoring the diametric and rotational angle ratios. FIG. 4
presents results for cases in which the interior mass of the
elastomer element is also elastomer material (upper surface 41) or
the elastomer element contains the metallic interior mass (lower
surface 43), which are the compositions exhibited in FIG. 2. It is
observed that for a given selection of rotational angle and
diametric ratios, the inclusion with elastomer inner mass possesses
the higher fundamental eigenfrequency. By strategically tailoring
these ratios, the eigenfrequency can be adjusted from values in the
100s of Hz to the buckling point (0 Hz), which stresses the
elastomer element at the elastic stability limit. The shape of this
fundamental mode, as well as the first buckling mode, is
exemplified in the finite element model results in FIG. 1b . From
the model predictions presented in FIG. 4, rotational angle ratios
at the limits of the current or available fabrication capabilities
(.alpha./.beta..apprxeq.0.7) are required to buckle the elastomer
elements within a reasonable amount of geometric constraint
D.sub.o/D.sub.i<1.05. As observed empirically, values of such
constraint above this amount may warp the elastomer topology at the
contact surface with the metal shell 11, thus violating the finite
element model assumptions and inhibiting uniform compressive stress
at the contact. The results in FIG. 4 also indicate that the
samples with metallic inner masses buckle for smaller values of
both ratios (lower surface 43) than those required for the samples
having the elastomer masses (upper surface 41). Considering the
rotationally-symmetric unit of the inclusion highlighted by the
dashed section in the top right inset of FIG. 4, each
radially-arrayed beam is axially constrained between the outer
metal shell 11 and the inner mass. It is known that the presence of
compliance in the boundary conditions of axially-loaded beams
increases the loads required to buckle the beam, which verifies the
finding here that the comparatively rigid metallic inner masses
require smaller diametric ratios to load the inclusions at the
elastic stability limit to exhibit desired hyperdamping effects.
Using the insights derived from the finite element model analysis,
hyperdamping metamaterials may be produced by embedding the
strategically designed inclusions 50 into 50.4 mm thick open cell
polyurethane foam 54 (such as that provided by Foam Factory, Inc.,
but not limited thereto), the foam 54 being cylindrical and having
a diameter of approximately 82 mm in two equal thicknesses.
Referring to FIG. 5, the foam 54 includes a centrally-located
crevice 56, which may be formed by extracted a portion of the foam
54 where a hyperdamping inclusion 50 according to principles of the
present invention is to be placed. The foam 54 and/or the
hyperdamping inclusion 50 may be secured via spray glue (such as,
but not limited to, HDX Spray Adhesive). A foam cylinder 54 formed
accordingly is illustrated in FIGS. 5A and 5B. Portions of the foam
54 extracted to form the crevice 56 or other foam, may be
positioned in the crevice 56 after placement of the hyperdamping
inclusion 50. The entire assembly may be secured, for example by
applying spray adhesive or glue into "one-piece". In forming the
"assembly", glue or spray adhesive is lightly applied so as to not
adversely impact the vibroacoustic properties of the polyurethane
foam. By this fabrication, the resulting hyperdamping metamaterial
specimen appears externally identical from the original cylinder of
foam from which it was derived, apart from a small seam of spray
glue visible around the perimeter. In addition, by extracting the
inner material, the foam is not under additional stresses once
re-assembled via the glue. In this example, the hyperdamping
inclusions 50 constitute a 2% volume fill ratio respecting the
whole metamaterial volume, and result in an effective metamaterial
specimen density of 48 kgm-3 (compared to the polyurethane foam
density 34 kgm-3). This is significantly less than the effective
density of recent metamaterials leveraging resonance- and
bandgap-based phenomena (around 1500 kgm-3 or >2000 kgm-3) and
is more comparable to the density of various acoustical materials
used in automotive and aerospace applications.
[0053] FIG. 5 shows a hyperdamping metamaterial specimen according
to principles of the present invention prior to assembly. FIG. 6
shows (b) force transmissibility and (c) absorption coefficient
experiment schematics.
[0054] By a linear elastic finite model, the primary vibration
modes of the inclusion 50 in the foam 54 occur around the frequency
band 175 to 275 Hz. For the metallic inner mass, these relevant
resonances are at the lower end of this band, while for the
elastomer mass they are at the higher end. As a result, the
greatest evidence of broadband energy absorption provided by the
hyperdamping metamaterials will be found within this bandwidth.
Above this frequency band, the modal density increases
significantly per octave and the higher frequency modes are mostly
associated with large deformations of the foam itself.
Traditionally, periodic metamaterials are designed to leverage the
lower frequency resonant modes for drastic vibroacoustic
attenuation at the specific eigenfrequencies. In contrast, the
hyperdamping metamaterial according to principles of the present
invention, using only a single inclusion, facilitates strongly
damped resonant properties in this frequency band, as well as at
higher frequencies where the modal density grows. The result is a
notably broadband, and hence robust, energy trapping and
attenuation effect.
[0055] To characterize the impact of the hyperdamping inclusions,
experiments were conducted with the foam on its own, having been
previously cut in half and re-assembled by spray glue, and also
with a conventional resonance-based metamaterial design that
includes the foam and a single inclusion consisting of lumped
elastomer (not shown) without radially arrayed beams cured in the
metal shell 11 referred to as the "resonant metamaterial". The
conventional approach is also similar to the strategy employed by
the previous studies on poroelastic metamaterials where lumped mass
(often metal) inclusions have been considered. All experiments are
carried out in an environmentally-controlled room at 22.8.degree.
C. and 37% humidity. The force transmissibility through and
acoustic absorption coefficient of the specimens are evaluated as
schematically shown in FIG. 6. The resulting force transmissibility
data represent the averaged result from 80 independent measurements
when the electrodynamic shaker (LabWorks, ET-140) was driven with
white noise filtered from 30 to 1500 Hz and data acquired using
input and output force transducers (PCB Piezotronics, 208C01). The
acoustic absorption data were derived from pressure measurements
taken in the impedance tube 65 with the acoustic source providing
white noise from 50 to 1600 Hz. Results from the 80 independent
measurements obtained from the two microphones 69 (PCB
Piezotronics, 130E20) were averaged, in accordance with ASTM
E1050-12, to derive the absorption coefficient.
[0056] FIG. 7 presents the results of force transmissibility
amplitude (left column) and acoustic absorption coefficient (right
column) for the poroelastic foam itself (dotted curves), the
resonant metamaterial (dashed curves, and see (c) top right
illustration), and the hyperdamping metamaterial (solid curves, and
see (c) top left illustration) using a diametric ratio of
D.sub.o/D.sub.i=1.051, elastomer inner mass, and rotational angle
ratio .alpha./.beta.=0.70. According to the finite element model
results shown in FIG. 4, this diametric ratio is in excess of the
ideal design at the elastic stability limit, and thus the
hyperdamping specimen used in the comparison of FIG. 7 is not
optimized. Optimization of the hyperdamping specimen may, in one
example, be realized by selecting diametric ratio and rotational
angle ratio from the finite element model results that are exactly
at the elastic stability limit, in which case the buckling point is
predicted. As described above, the modes associated with large
displacement of the total mass of the exemplary inclusion occur in
the frequency band 175 to 275 Hz, while modes below and above this
range are mostly associated with large deformations of the foam
itself. Thus, in FIG. 7(a), the measurements of force
transmissibility (FT) reveal great similarity in response trends at
frequencies outside of this range, while in the range there are
notable differences to consider. For instance, the narrowband force
transmissibility shows that the resonant and non-optimized
hyperdamping metamaterials provide approximately similar reductions
across the 175 to 275 Hz band, compared to the force
transmissibility of the foam itself. This frequency band is
associated with the principal resonant modes associated with large
displacement of the total mass, as described above. However,
considering the 1/3-octave band results showin in FIG. 7(b), from
200 to 630 Hz, the hyperdamping metamaterial provides an average of
1.2 dB greater force transmissibility reduction than the resonant
metamaterial.
[0057] In addition, the absorption coefficients in the narrowband
and 1/3-octave band comparisons of FIGS. 7(c) and 7(d),
respectively, reveal similar enhancement of the acoustic wave
attenuation by virtue of the inclusions. The results illustrated in
FIGS. 7(c) and 7(d) show that a non-optimized hyperdamping
metamaterial can provide comparable or greater absorption of
vibroacoustic energy than a counterpart, resonant metamaterial, all
the while the hyperdamping inclusion design constitutes only 48% of
the mass of the resonant inclusion.
[0058] FIG. 7 shows measurements of narrowband and 1/3-octave band
results of (a,b) force transmissibility amplitude (FT) and (c,d)
acoustic absorption coefficient. Comparison is made among the
(dotted curves) poroelastic foam itself, (dashed curves) the
resonant metamaterial with lumped elastomer and shell inclusion
(see (c) top right illustration), and (solid curves)
[0059] Having assessed the merits of the hyperdamping concept with
respect to the conventional resonant metamaterial approach, we next
evaluate the impact of more effective hyperdamping inclusion design
according to principles of the present invention as informed from
the finite element model results of FIG. 4. In this way, we test
the foundational hypothesis of this research that inclusion designs
nearest to the elastic stability limit cultivate the greatest
damping effects. FIG. 8 shows measurements of force
transmissibility amplitude (FT). Dotted curves denote results for
the control specimen; solid curves denote results for the
hyperdamping metamaterial with elastomer inner mass; dashed curves
denote results for the hyperdamping metamaterial with metallic
inner mass. Narrowband and 1/3-octave band results for the
hyperdamping specimen designs having diametric ratio (a,b)
D.sub.o/D.sub.i=1.020 , (c,d) D.sub.o/D.sub.i=1.035, and (e,f)
D.sub.o/D.sub.i=1.066.
[0060] By the reductions in the force transmissibility amplitude
with respect to the specimen consisting of only poroelastic foam,
the measurements in the top row in FIG. 8 show that the broadband
energy absorption and attenuation is prominent across the range of
about 175-225 Hz for the hyperdamping specimens having the metallic
inner mass, FIG. 8(a), while for the specimens with elastic inner
mass the energy capture is more apparent around 200-275 Hz, FIG.
8(c). The finite element model results in FIG. 4 indicate that the
critical design point occurs for smaller values of the diametric
ratio D.sub.o/D.sub.i using the metallic inner masses, when the
rotational angle ratio .alpha./.beta. is held constant. The force
transmissibility measurements in both the narrowband and 1/3-octave
evaluations of FIG. 8 verify this design methodology. Namely, the
hyperdamping metamaterial with metallic inner mass generates
greater broadband energy dissipation for the smaller ratio
D.sub.o/D.sub.i=1.020 (29.1% mean reduction of FT in 1/3-octaves
from 157 to 630 Hz with respect to the control specimen) while the
specimen with elastomer inner mass yields maximum broadband
performance for a greater ratio D.sub.o/D.sub.i=1.035 (41.2% mean
enhancement of FT reduction in 1/3-octaves from 250 to 630 Hz with
respect to the control specimen). The reductions to force
transmissibility well above the primary resonances of the
inclusions in the poroelastic material are due to the increasing
modal density, which occurs above about 275 Hz, thus introducing
means to magnify the energy dissipation properties in the mid
frequency range. These are significant increases in the broadband
absorbed and attenuated vibration energy, particularly considering
that the hyperdamping inclusions account for only 2% of the total
specimen volume.
[0061] These enhancements to the energy dissipation are reduced if
the diametric ratio is changed to be deliberately away from the
elastic stability limit. For example, the specimens having the
metallic inner masses are less effective in the broadband reduction
of FT when D.sub.o/D.sub.i>1.020, FIGS. 8(c) and 8(e), which
corresponds to post-buckled configurations of the elastomer element
as observed empirically; specimens with elastomer inner masses have
reduced energy attenuation performance for
D.sub.o/D.sub.i>1.035, FIG. 5(e), which likewise corresponds to
post-buckling of the elastomer element. These results validate the
hypothesis of this research that the hyperdamping effects are due
to the extreme softening of the inclusions and not simply to
compressing the inclusions beyond the buckling point.
[0062] FIG. 9 shows measurements of absorption coefficient. Dotted
curves denote results for the poroelastic foam-only "control"
specimen; solid curves denote results for the hyperdamping
metamaterial with elastomer inner mass; dashed curves denote
results for the hyperdamping metamaterial with metallic inner mass.
Narrowband and 1/3-octave band results for the hyperdamping
specimen designs having diametric ratio (a,b)
D.sub.o/D.sub.i=1.035, (c,d) D.sub.o/D.sub.i=1.051, and (e,f)
D.sub.o/D.sub.i=1.066.
[0063] The top row of FIG. 9 presents narrowband measurements of
absorption coefficient, while the bottom row provides the
corresponding 1/3-octave band results. Of note, the polyurethane
foam is itself very acoustically absorptive such that enhancement
of this property using a single, embedded hyperdamping inclusion
appears to be a challenging goal at the outset. Yet, as seen in the
top row of FIG. 6, due to the presence of the hyperdamping
inclusions the absorption coefficient of the baseline poroelastic
foam is increased from frequencies of about 400 to 1400 Hz, across
which the modal density is sufficiently great. This improvement is
greater for the inclusions having metallic masses when employing
the smaller value of the diametric ratio, FIG. 6(a),
D.sub.o/D.sub.i=1.035 which agrees with the FE model predictions.
Using this inclusion composition, across the 500 to 1260 Hz
1/3-octave bands the mean absolute enhancement of the absorption
coefficient over control specimen levels is 0.063, as shown in FIG.
9(b).
[0064] Hyperdamping inclusions with elastomer inner masses
according to principles of the present invention are more effective
at increasing the energy dissipation (and hence absorption
coefficient) for a greater value of diametric ratio, FIG. 9(c),
yielding a mean absolute absorption coefficient improvement from
the control specimen results of 0.045 across the 500 to 1260 Hz
1/3-octave bands, FIG. 9(d). Indeed, for both of the exemplary
designs that strategically leverage the hyperdamping effect, the
increase in the absorption coefficient over the control specimen is
generally uniform across this broad frequency band, FIGS. 9(e) and
9(f) show that the performances of the specimens are reduced from
the peak achievements realized when the elastomer elements are
compressed around the elastic stability limit, for example, when
the inclusions are constrained by diametric ratios greater than the
exemplary values. The exceptional softening of the inclusion design
is the origin of the hyperdamping effects, which invests the
metamaterial with remarkable, broadband vibroacoustic energy
dissipation properties using a negligible change (2%) to the host
media volume due to the embedded inclusion.
[0065] The finite element (FE) model to study the effective
topological composition of the hyperdamping inclusions utilizes the
geometry exemplified in FIG. 4 at the top inset, assuming plane
strain conditions apply for a first approximation of the principal
eigenfrequencies and modes. Material properties are therefore
required for inner metal cylinders (if applicable) and for the
elastomer elements. The steel metal cylinders are modeled as a
linear elastic material having density, Young's modulus, and
Poisson's ratio, respectively, .rho.=7800 kgm-3, =200.times.109 Pa,
and .nu.=0.30. Previous studies have indicated that similar
variants of the silicone used here to create the elastomer elements
are adequately characterized using Neo-Hookean, hyperelastic
material models. In such cases, the strain energy density is
expressed using
W=1/2 .mu..sub.0( .sub.1-3)+1/2K.sub.0(J-1).sup.2
[0066] where .mu..sub.0 and K.sub.0 are the initial shear and bulk
moduli, J=det F is the determinant of the deformation gradient
F=.differential.x/.differential.X found respecting the current x
and reference X configurations, and .sub.1=tr(F.sup.TF) is computed
from the distortional tensor F=(J.sup.1/3I).sup.-1F where I is the
identity matrix .left brkt-bot.1.right brkt-bot.. For the silicone
material employed in this research, representative parameters of
.mu..sub.0=250 kPa and K.sub.0=6.25 MPa are employed in the FE
computations while the density is .rho.=1145 kgm-3 as measured. The
boundary conditions constrain the normal displacement of the
elastomer element outer diameter in accordance with the constraint
imposed by the ratio D.sub.o/D.sub.i. An eigenfrequency analysis is
carried out to evaluate the influence upon the lower-order
eigenfrequencies due to the variation in the ratios .alpha./.beta.,
which characterizes the unconstrained topology of the elastomer
element, and D.sub.o/D.sub.i, which quantifies the nearness to the
critical buckling stress upon the elastomer element topology.
However, a design theme of the heretofore described examples is
that sculpted beams that support an internal mass must be arrayed
radially from the inclusion center, otherwise the compression
provided by the geometric shell constraint would be prevented from
causing a buckling of the topology. To illustrate the change in the
lower order eigenfrequencies in consequence to the constraint
imposed by the metal shell, FIG. 10 shows results from this finite
element model for the case in which the rotational angle ratio
.alpha./.beta.=0.70 while the diametric ratio D.sub.o/D.sub.i is
varied. From the finite element model results at right, it is
evident that the second, third, and fourth eigenfrequencies do not
significantly change due to the critical stressing that occurs when
the elastomer element topology is designed to lead to buckling
effects.
[0067] FIG. 10 shows a comparison of eigenfrequency variation among
the four lowest eigenfrequencies (at left) and the corresponding
mode shapes (at right). The dotted curves at right indicate that
the inner mass of the inclusion is metallic while the solid curves
indicate results when the inner mass is composed of the elastomer
material.
[0068] The finding that the second, third, and fourth
eigenfrequencies do not significantly change due to the critical
stressing may be explained by the fact that these mode shapes are
not rotationally symmetric, as shown in the right part of FIG. 10,
while the constraint that leads to buckling is one which uniformly
applies to the elastomer element around the full perimeter.
[0069] A finite element model can be used to assess the
distribution of the structural eigenfrequencies and modes for the
hyperdamping inclusion once embedded into the polyurethane foam. By
such an evaluation, one is able to more effectively assess the
impact of the inclusions since the greatest magnification of the
damping effects are around the frequencies associated with these
resonances, assuming they are significantly excited by the source
input. As observed macroscopically, the result will be that these
resonances, often associated with resonance-based metamaterials,
will appear to be strongly damped.
[0070] The finite element model geometry is the same as the
experimental geometry as detailed with respect to FIGS. 5 and 6. In
this model, the polyurethane foam is considered to be a linear
elastic material. Thus, poroelastic coupling is neglected, which is
justified by the focus on small-amplitude, relatively low frequency
force transmissibility and acoustic-elastic wave propagation, where
the linear elastic characteristics of the polyurethane foam are
more apparent. The polyurethane material properties are given to be
.rho.=30 kgm-3, E=7.times.10.sup.4 Pa, and v=0.41. The inclusion is
modeled as an effective lumped mass of uniform density, Poisson's
ratio v=0.33, and high stiffness E=200.times.10.sup.9 Pa in
accordance with the assumption that it is only a cylindrical mass
embedded into the foam. The uniform density of this mass is
therefore the average mass of the inclusions for a given D.sub.o
(whether with inner elastomer or metallic cylindrical mass) divided
by the inclusion volume. Consideration of the inclusion as a
uniform body is theoretically justified by the fact that the
vanishing fundamental eigenfrequency of the hyperdamping inclusion
means that the natural frequencies of the composite inclusion
components (shell and elastomer element) as embedded into the foam
media are primarily due to the total dynamic mass of the composite.
This contrasts to considering the inclusion internals as possessing
additional degrees of freedom; under the unique condition of the
buckling constraint which yields the hyperdamping effects, the
vanishing principal stiffness contribution indicates that the
effective response of the inclusion is significantly first-order
and more representative of a damping effect rather than like an
additional mass-spring-like degree of freedom.
[0071] In this finite element model, one circular surface of the
metamaterial is fixed while the opposing circular face is free to
move in the direction normal to the surface but may not rotate. The
results of the finite element analyses are shown in FIG. 11 in
terms of the kinetic energy density associated with each
eigenfrequency. FIG. 11 illustrates eigenfrequency distribution and
corresponding kinetic energy density of the mode. Squares indicate
the results in which the lumped cylindrical inclusions are
characterized according to the average density of hyperdamping
inclusions with elastomer inner masses, while the circles denote
the result respecting hyperdamping inclusions with metallic inner
masses. Thus, the plot provides information on the spectral
distribution of the eigenmodes, as well as of the significance of
the global system energy associated with the mode. The square data
points indicate the FE model results in which the lumped
cylindrical inclusions are characterized according to the average
density of hyperdamping inclusions with elastomer inner masses
(approximately 1238 kgm-3), while the circles denote the results
respecting hyperdamping inclusions with metallic inner masses
(approximately 2090 kgm-3). The modes are found to be the result of
three primary phenomena. The lowest frequency mode in each case is
associated with uniform (in-phase) compression/elongation of the
metamaterial and inclusion. A mid frequency range of modes occurs
wherein the inclusions are seen to exhibit large deformations
and/or rotations within the foam, while the corresponding
eigenfrequencies occur at values corresponding to the total
inclusion mass (and are thus distinct comparing the two inclusion
types shown in FIG. 11). As a result of these large excursions of
the inclusions, the greatest broadband damping effect is
anticipated to occur in this bandwidth around 175 to 325 Hz.
Finally, a higher frequency range of modes occurs characterized by
large deformations of the foam while the inclusions are relatively
stationary. Since there is comparatively little displacement of the
inclusions in contribution to these modes, they occur at almost the
same frequencies when considering the two types of inclusions
evaluated in FIG. 11. These results exemplify the fact that energy
trapping occurs primarily at the lower frequencies associated with
a select number of resonances possessing high kinetic energy
density while at high frequencies the energy loss is due to highly
modal density resulting in stochastic-like vibrations that
resistively dissipate energy. Thus, this helps to explain why the
energy trapping appearing in the force transmissibility experiments
(FIGS. 4 and 5 main text) is mostly localized in the frequency band
<600 Hz while the absorption coefficient measurements (FIGS. 4
and 6 main text), which do not significantly excite lower frequency
modes, give greater indications of the high frequency losses
associated with the lower-energy and higher frequency modes that
are finely spaced apart in the spectrum.
[0072] Force transmissibility experiments were conducted using the
arrangement shown in FIG. 12. The experiments are carried out on an
optical isolation table to prevent potential building motions from
interfering with the measurements. White noise filtered from 30 to
1500 Hz is used to drive the electrodynamic shaker which acts on
the input force transducer. An output force transducer is attached
to a grounded, rigid aluminum frame. As illustrated in FIGS. 5 and
6 and as shown in FIG. 12, the force transducers are affixed to
force expanders composed from acrylic PMMA which are many orders of
magnitude stiffer than the polyurethane foam. The expanders'
stiffness inhibits the possibility that the measured forces are
different than those transmitted to the hyperdamping metamaterial
specimens. The expanders also ensure that the force is equally
distributed across the full surfaces of the cylindrical
metamaterial specimen so as to evaluate only the one-dimensional
force transmissibility property of the specimens through their
thickness. Acquired data are sampled at 16384 Hz and are filtered
from 20 to 2000 Hz using a fourth-order bandpass infinite impulse
response filter prior to further computation. Then, the force
transmissibility of the 80 independent measurements is determined
and the average of the results is taken. One-third-octave band
values are taken in conformance to traditional methods.
[0073] Absorption coefficient measurements were taken using the
impedance tube setup as shown in FIG. 13. The tube length from
acoustic source to specimen surface is approximately 575 mm. The
cylindrical metamaterial specimens are mounted in a way such that
the surface of the specimen which faces the propagating wave is
normal to the direction of wave propagation, ensuring that
reflections are likewise normal. Data from the microphones are
sampled at 51200 Hz and filtered from 20 to 2000 Hz using a
fourth-order bandpass infinite impulse response filter prior to
further computation. Then, the acoustic absorption coefficient as
determined from the 80 independent measurements is averaged.
One-third-octave band values are computed according to traditional
methods.
[0074] Although the elastomeric inclusions are described embedded
in poroelastic foam, favorable damping properties exhibited through
use of the elastomeric inclusions according to principles of the
present invention do not require the surrounding poroelastic foam
as illustrated in FIG. 3. Instead the favorable damping properties
are exhibited by the constrained elastomer inclusion itself in
whatever application it is employed.
[0075] As another example application, this inclusion design may be
directly embedded into structural panels, such as dash or trim
panels in vehicular systems, where flexural vibrations and
transmitted sound will be extremely abated. Another example would
be to use a constraint imposed by pre-load/stress (such as occupant
weight on a seat cushion or engine weight on engine mount) to
simplify the design to utilize only the inclusion component (i.e.,
no `shell` component) while the radially-arrayed beams of the
inclusion topology are nearly buckled in consequence to the
surrounding, pre-load/stress.
[0076] In fact, elastomeric materials are in common use as dampers,
isolators, or fillers due to their large damping provided at
mid-to-high frequencies. An advantage of an elastomer inclusion
according to principles of the present invention is that the
sculpting of the elastomer removes material from the underlying
non-engineered bulk elastomer material, making the hyperdamping
materials lighter in weight than their counterparts. Moreover, as
shown in FIG. 3, the hyperdamping materials attenuate greater
structure-borne sound energy at low frequencies than the baseline
non-engineered bulk elastomer materials. These factors show that
elastomer inclusions according to principles of the present
invention provides higher energy attenuation performance using less
material mass than existing vibration/noise control treatment
approaches.
[0077] In order to achieve the advantages of the present inclusion,
the shell or "constraint" needs to be effectively rigid with
respect to the inclusion material that is constrained to achieve
the near-buckling described herein. To that end, the constraint
does not need to be a different material. If the whole system is an
elastomer and somewhere within the elastomer is the architecture of
the radially-arrayed beams or similar beam constituents (they could
be in a line of beams, for instance similar to column arrangements
in architectural contexts), then when that whole elastomer system
is under pre-load, the internal beam sub-components will be much
more stressed than the whole and will nearly buckle, as is desired
to yield the hyperdamping effect. The choice of the constraint
material can be chosen according to final engineered product,
provided that it achieves the desired pre-load.
[0078] As illustrated in FIGS. 14 and 15, acoustic absorption
coefficient and force transmissibility are compared for cylindrical
samples of poroelastic foam with or without inclusions. One
exemplary inclusion is considered a "control." This exemplary
control inclusion consists of a solid cylinder with elastomer that
has been poured inside of a metal shell. The other exemplary
inclusion considered is a "hyperdamping inclusion" made from the
same "batch" of elastomer that was used for the control inclusion,
but made according to principles of the present invention. Yet, by
the strategic sculpting and design, the hyperdamping inclusion is
only about 48% of the mass of the control, indicating a great
weight savings.
[0079] Experimental measurements of acoustic absorption coefficient
of the control inclusion and the inclusion according to principles
of the present invention are presented in FIG. 14. Over almost all
of the frequencies, the hyperdamping inclusion provided increased
absorption coefficient, and thus increased attenuation of air-borne
acoustic energy, than both the poroelastic foam alone and the
poroelastic foam with the control inclusion. The noise reduction
coefficient (NRC) from 250 to 1,000 Hz of the control material is
0.50 in comparison to the NRC from 250 to 1,000 Hz for the
hyperdamping material of 0.60. The narrow band measurements of
force transmissibility through the samples are shown in FIG. 15.
FIG. 16 shows the corresponding one-third octave band reductions in
force transmissibility from the foam-only case.
[0080] The wide-band reductions in transmissibility seen in FIG. 15
as provided by the hyperdamping material/inclusion indicate a
substantial increase in the structure-borne sound attenuation
compared to the poroelastic foam-only and the control material
sample. The enhanced transmissibility reductions are verified in
the one-third octave band evaluations in FIG. 16, showing that the
lighter weight hyperdamping material provides significantly greater
broadband vibration and acoustic energy attenuation. These
exceptional properties--lightweight, and high damping across broad
frequency bandwidth--are derived from the strategic designs and
manufacturing methods of the hyperdamping inclusions as described
herein.
[0081] According to the design, the constituent that is stressed or
loaded near the elastic stability limit is not limited to be an
elastomer. Elastomer is utilized for proof-of-concept specimens due
to its high compliance compared to the metal shells that provide
geometric constraint, which results in a `room-for-error` in
design. Stiff or metallic structures at the elastic stability limit
may be used to realize the hyperdamping effect with appropriate
control of tolerances. Materials softer than the
previously-described elastomer for the hyperdamping inclusion, such
as a sculpted foam, may be used to realize the hyperdamping effect,
given appropriate attention to the fact that increased compliance
of the softer materials may result in the need for appropriate
tolerance control. Such flexibility for material selection enables
broad implementation opportunities.
[0082] Acoustic and/or elastic wave attenuation pertains to
vibrations at all frequencies, wave propagation at all frequencies,
and transient phenomena such as impulsive and blast energies.
[0083] Acoustic and/or elastic wave attenuation by embedding or
sculpting inclusions according to an aspect of the present
invention within host media (where the inclusions are the same
material as the host media) and where the host media is under
static pre-load, thus omitting use of additional constraint layer
(e.g. metal shell described). Such "unconstrained" inclusion is
illustrated in FIG. 1 separated from the metal shell. This
implementation creates an internal one-degree-of-freedom internal
system that can attenuate waves, vibrations, shock, and sound.
[0084] Such unconstrained device can be used in various
applications, such as, but not limited to: architecting polystyrene
foam acoustic/thermal insulation with the beam sub-components that
is pressed between studs and drywall in homes; concrete road
surfaces with internal beam-like architectures that better
attenuate road noise, and using similar concepts in concrete road
noise barriers that have high static pre-load by virtue of their
self-mass; sculpting the foam of a vehicle seat, such as in cars,
to have internal beam-like architecture so that when an occupant
rests on the seat, the pre-load provided by the individual serves
to compress/constrain the beams near to their buckling point
resulting in a large suppression of energy to the seated occupant
when the seat is excited by input vibrations and shock; sculpting
carpets, pads, and other floor coverings that are underload by
virtue of moving mass (people walking, objects rolling, etc), and
building insulation materials for large sound transmission loss
between rooms and residences
[0085] The inclusion geometry of beams that is created within the
carpet/pad/covering material can be designed to be constrained near
to the buckling point for a range of supported loads so that energy
is less transferred through the carpet/pad/covering and to the
floor below (such as to an under-story residence); in other
automotive, civil, aerospace, space, marine, or rail applications
where all-metal realizations of the concepts are desired, the
geometry of slender internal beams may be machined or otherwise cut
into a host material such as a metal or plastic or wood, carpets
and pads in vehicle systems, such as aircraft or automobiles, to
deaden structure-borne noise (i.e. vibration and wave energies that
may also radiate to become sound).
[0086] Filler material for sandwich panels, such as filler for
aluminum honeycomb panels in aircraft, to dissipate operational
vibrations. When the system is subjected to excitations and loads,
the internal components undergo greater oscillation by virtue of
the locally reduced stiffness (associated with the near buckling
beam elements) and thus provisioning the system with anomalous
damping properties associated with these elements.
[0087] Acoustic and/or elastic wave attenuation by embedding or
sculpting inclusions according to an aspect of the present
invention and held within constraining layers/shells, such as a
metal shell, within host media that are under static pre-load. The
use of the constraining layer or shell is to provide for added
resonant mass and generates a two-degree-of-freedom internal system
that can attenuate waves, vibrations, shock, and sound, with
potential for greater effect at low frequencies than the above
examples. These inclusions are thus self-enclosed and can be
injected or otherwise inserted into other media.
[0088] Such constrained devices can be used in various
applications, including those listed above, as well as, but not
limited to: foam insulation in building construction wherein such
inclusions are a part of the foam-making (blowing) process and
become members of the foam layer; room and office partitions,
cubicle dividers, and so on with internal inclusions for enhancing
noise insulation properties. An inclusion according to these
principles provides for broadband and low frequency noise control
enhancement and thus may be used in any structure where such
frequency damping is desired.
[0089] Acoustic and/or elastic wave attenuation by embedding
inclusions within structural members, where the latter members
serve as components of a greater system. For example, inclusions
according to principles of the present invention may be used within
vehicle frame component, such as the subframe, A- or B- pillars,
and other automotive components; in aerospace/space components as
in within sandwich panels (that are a staple aircraft construction)
or within the stingers of aircraft wings, and in rail-transport
frame members having hollow geometries. These inclusions may be
inserted into all such geometries and be naturally compressed
within the host geometry. For instance, the subframes of
automobiles often have cylindrical-like extruded geometries wherein
a conventional cylindrical hyperdamping inclusion may be designed
and embedded. Thus, when the host system is under acoustic/elastic
wave excitations, the embedded hyperdamping inclusions will
effectively attenuate the energies prior to their delivery further
downstream to delicate vehicle locations (such as an occupant seat
attached to a vehicle chassis).
[0090] Inclusions according to principles of the present invention
may be used in civil or structural engineering applications where
C, U, and box-beam members compose the structure. Into such C, U,
or box channels can be inserted the inclusions that would be
targeted to be under the desired compression constraint to yield
near-buckling of the beam components. Thus, when the structure is
under wind or seismic or machine-induced loads (like HVAC on roof),
the inclusions can abate transfer of the energy into motions of the
structure by the damping of energy at the inclusion.
[0091] Inclusions according to principles of the present invention
may be used in applications of seals, where the seal is compressed
in order to prevent leakage of flow of liquid or gas but the
compressed structural piece (such as a cap, door, or trim) is also
desired to not vibrate due to exterior structural or acoustic
loads. Thus, the hyperdamping-type seal may have a cross-section
geometry that includes beam components that when under the working
condition of the seal (where it is compressed) both provides the
demanded flow prevention and enhances damping of the structural
piece that compresses it down via the greater damping properties
borne out by the compressed internal geometry.
[0092] Inclusions according to principles of the present invention
may be used as shock/vibration absorbers for electronics where the
hyperdamping inclusions serve to support the load of the
electronics while promoting large attenuation of the input energy
from transmitting to the supported layer of electronics. The
inclusions would be designed such that their supported load or
pre-compression extent capitalizes on the hyperdamping
phenomenon.
[0093] Examples of uses for inclusions according to principles of
the present invention are illustrated in FIGS. 17-19, and include
vehicle panels, seats and in space launch vehicles. These examples
are by no means intended to be limiting.
[0094] For example, FIG. 17 illustrates elongated tubular
inclusions 170 according to principles of the present invention
incorporated into vehicular structural panels. As can be
appreciated from the figures, the tubular inclusions 170 include
voids. The near buckling constraint on the tubular inclusions may
be provided by an external cylindrical shell or the near buckling
constraint may be imparted by load provided by components, such as
walls 174, of the structural panel itself
[0095] As illustrated in at least FIG. 18, hyperdamping material
including appropriate voids to impart the beam-like properties
according to principles of the present invention may be included in
a structural design, where the near buckling condition is provided
by external load-providing structures, such as spacing panels or
walls at the boundary of the hyperdamping material 184.
[0096] As illustrated in at least FIG. 19, hyperdamping inclusions
including appropriate voids to impart the beam-like properties
according to principles of the present invention may be included in
a structural design for other vibration environments, such as space
launch vehicles. As can be appreciated from the figures, the
inclusions 190 include voids. The near buckling constraint on the
tubular inclusions may be provided by an external shell or the near
buckling constraint may be imparted by load provided by components,
such as walls, of the structural panel itself
[0097] As employed here, "hyperdamping" indicates an unusually
large proportion of damping forces, with respect to inertial and
stiffness-based forces, in consequence to design- or
constraint-based factors imposed upon an intelligently architected
inclusion topology. In the present implementation, the selection of
diametric ratio for a given elastomer element topology enables the
extreme softening which is characteristic of loading conditions at
the elastic stability limit. Other researchers have realized
similar anomalous dissipative phenomena via applied compressive
stress, ferroelectric domain switching, and temperature control.
Contrasting these approaches, the strategy employed here to realize
hyperdamping within the poroelastic media is passive,
non-destructive to the host material, and not subject to major
deviation over time by hysteretic influences, thus making the
proposed hyperdamping metamaterials more viable for practical
applications. Moreover, this study focuses on the impact of an
individual inclusion upon the resulting vibroacoustic properties of
the metamaterial. This contrasts with previous studies that have
exemplified the roles of periodicity towards magnifying the energy
absorption possible in resonant metamaterials or phononic crystals.
Yet, based on the experimental evidence described herein,
substantial broadband energy trapping and attenuation is achievable
even when employing just one hyperdamping inclusion at a 2% volume
fill in the poroelastic media.
[0098] Principles of the present invention provide hyperdamping
metamaterials to realize broadband energy trapping and attenuation,
while retaining the advantages of a lightweight solution viable for
diverse noise and vibration control applications. Because the
hyperdamping effects are not reliant upon the resonance- or
bandgap-based phenomena of conventional metamaterials and phononic
crystals, the effectiveness of the energy attenuation is more
robust for working conditions where the peak frequencies of
vibroacoustic energy may vary in time. In this way, the
lightweight, hyperdamping metamaterials have practical benefits
over contemporary counterparts.
[0099] Embodiments of the present invention provide lightweight,
hyperdamping metamaterials that interface with the acoustic free
field to achieve large vibration and acoustic wave energy
attenuation.
[0100] While various embodiments of the present invention have been
described above, it should be understood that they have been
presented by way of example only, and not limitation. It will be
apparent to persons skilled in the relevant art that various
changes in form and detail can be made therein without departing
from the spirit and scope of the present invention. Thus, the
breadth and scope of the present invention should not be limited by
any of the above-described exemplary embodiments, but should be
defined only in accordance with the following claims and their
equivalents.
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